Subject: Electron density at nucleus/field shift

From: Stephen Cooke <[email-masked]>
Date: Thu, 23 Jan 2003 17:22:18 -0800 (PST)

Here is my situation.

In a 1982 paper by Knockel et al. (Chem. Phys. 68, 1982, pages 21-28) the 
authors employed a Hartree-Fock method to determine, for lead sulfide 
(PbS), the derivative of the electron density at the Pb nucleus with 
respect to the internuclear separation and then evaluate this derivative 
at the equilibrium bond length.

I would like to perform the same calculation for a number of other heavy 
metal containing diatomics.  To do this I have used g98 with the following 
input as a test of my method:

# uhf/LANL1DZ Density=Current Cube=101 TEST

PbS

0 1
Pb 0.0 0.0 0.0
S  2.1 0.0 0.0

pbi.cub

I run this input 10 times, each time with a different Pb-S bond length.
(As you can see its a very simple calc. and it doesnt take long to run).  
> From each output I extract the electron density at the Pb nucleus from the 
grid using a short FORTRAN code.  In this extraction it is necessary for 
me to fit a polynomial to the data and then interpolate for the result at 
the Pb nucleus.

I then fit a polynomial to the data (internuclear separation vs. 
electron density at the nucleus) take the derivative of the fitted 
equation and evaluate this derivative at the equilibrium bond 
length (2.2851).  In doing this i get the number -8.984E-05 
and i believe the units are bohr^-4.  The value quoted by Knockel et 
al. is closer to +40 angstroms^-4 (!).  In my calculation the 
elec.density at the Pb nucleus is small and from the gradient is 
clearly decreasing over the increasing internuclear separation
I have examined (2.1 - 2.6 angstroms).  Knockels 
results indicate the exact opposite!  

My assumption is that i am doing the calculation incorrectly (Im a bit 
green at this). I also have some uncertainties i.e. Is the density 
that im calculating including the core electrons (nb. I get the 
same answer as above if i use the core=full keyword), will the 
effective core potential for Lead affect my results?

My ultimate aim, like Knockel et al., is to evaluate the extent of field 
shift effects upon the rotational energy of a diatomic molecule.  With 
respect to calculating the above I really only need ball park estimates / 
trends to help me analyse our experimental data.

I would be very grateful of any help that anybody could offer and will of 
course summarise any responses i receive.

Steve Cooke
[email-masked]